Finite Group Databasebeta

← C2×#20287277 #28262772

Subgroups — C2×#20287277 #28262772

Order 13568.

1898 conjugacy classes of subgroups.

The subgroup lattice has 736 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16811319C211yesmaximal, characteristic
2C2×#16811313C211yesmaximal, characteristic, complemented
3#20287277C2116yesmaximal, direct product factor
4C2×#16811025C211yesmaximal, characteristic, complemented
5C2×#16810942C211yesmaximal, characteristic, complemented
6C2×#16810965C211yesmaximal, characteristic, complemented
7C2×#16810948C211yesmaximal, characteristic, complemented
8C2×#16810954C211yesmaximal, characteristic, complemented
9C2×#16810931C211yesmaximal, characteristic, complemented
10C2×#16810924C211yesmaximal, characteristic, complemented
11C2×#16810869C211yesmaximal, characteristic, complemented
12C2×#16810869C211yesmaximal, characteristic, complemented
13C2×C4×#11719913C211yesmaximal, characteristic, complemented
14C2×#16810665C211yesmaximal, characteristic, complemented
15C2×#16810665C211yesmaximal, characteristic, complemented
16C2×C53×#436C211yesmaximal, characteristic, complemented
17C22×#11719913C2211yescharacteristic
18#16811319—24no—
19#16811319C2218yes—
20#16811313—24no—
21#16811313C2218yescomplemented
22C2×#13133212—21no—
23C2×#13133210—21no—
24C2×#13133209C2211yescharacteristic
25C2×#13133209C2211yescharacteristic
26C2×#13133207—21no—
27C2×#13133199—21no—
28C2×#13133198—21no—
29C2×#13133196C2211yescharacteristic
30C2×#13133196C2211yescharacteristic
31C2×#13133191C2211yescharacteristic
32C2×#13133191C2211yescharacteristic
33C2×#13133189—21no—
34C2×C4×Dic106C2211yescharacteristic
35C2×C4×D212C2211yescharacteristic
36C2×#13133177—21no—
37C2×#13133176C2211yescharacteristic
38C2×#13133176C2211yescharacteristic
39C2×#13133173—21no—
40C22×C4⋊Dic53C2211yescharacteristic
41C22×C4⋊Dic53C2211yescharacteristic
42#16811025C2218yescomplemented
43#16810965C2218yescomplemented
44#16810954C2218yescomplemented
45#16810948C2218yescomplemented
46#16810942C2218yescomplemented
47#16810931C2218yescomplemented
48#16810924C2218yescomplemented
49#16810869C2218yescomplemented
50#16810869C2218yescomplemented
51C4×#11719913C2218yescomplemented
52#16810665C2218yescomplemented
53#16810665C2218yescomplemented
54C2×#13133151C2211yescharacteristic
55C2×#13133151C2211yescharacteristic
56C2×#13133151C2211yescharacteristic
57C2×#13133151C2211yescharacteristic
58C2×#13133149C2211yescharacteristic
59C2×#13133149C2211yescharacteristic
60C2×#13133149C2211yescharacteristic
61C2×#13133149C2211yescharacteristic
62C2×#13133149C2211yescharacteristic
63C2×#13133142C2211yescharacteristic
64C2×#13133142C2211yescharacteristic
65C2×#13133142C2211yescharacteristic
66C2×#13133139C2211yescharacteristic
67C2×#13133139C2211yescharacteristic
68C2×#13133139C2211yescharacteristic
69C22×M16×C53C2211yescharacteristic
70C22×M16×C53C2211yescharacteristic
71C2×C4×D4×C53C2211yescharacteristic
72C53×#436C2218yescomplemented
73C2×C4⋊C8×C53C2211yescharacteristic
74C2×C22⋊C8×C53C2211yescharacteristic
75C2×C22⋊C8×C53C2211yescharacteristic
76C2×C4×C8×C53C2211yescharacteristic
77C22×Dic106C2311yescharacteristic
78C22×D212C2311yescharacteristic
79C22×C22⋊D53—21no—
80C22×C22⋊D53—21no—
81C23×Dic53—21no—
82C23×Dic53—21no—
83C22×C4×D53—21no—
84C2×#11719913—24no—
85C2×#11719913C2314yes—
86#13133212—28no—
87#13133210—28no—
88#13133209—22no—
89#13133209—22no—
90#13133209C2314yes—
91#13133209C2314yes—
92#13133207—28no—
93#13133199—28no—
94#13133198—28no—
95#13133196—22no—
96#13133196—22no—
97#13133196C2314yes—
98#13133196C2314yes—
99#13133191—22no—
100#13133191—22no—
101#13133191C2314yes—
102#13133191C2314yes—
103#13133189—28no—
104C4×Dic106—22no—
105C4×Dic106C2314yes—
106C4×D212—22no—
107C4×D212C2314yes—
108#13133177—28no—
109#13133176—22no—
110#13133176—22no—
111#13133176C2314yes—
112#13133176C2314yes—
113#13133173—28no—
114C2×C4⋊Dic53—22no—
115C2×C4⋊Dic53—22no—
116C2×C4⋊Dic53—21no—
117C2×C4⋊Dic53—21no—
118C2×C4⋊Dic53C2314yes—
119C2×C4⋊Dic53C2314yes—
120C2×C4⋊Dic53C2311yescharacteristic
121C2×C4⋊Dic53C2311yescharacteristic
122C2×C4⋊Dic53C2311yescharacteristic
123C2×C4⋊Dic53C2311yescharacteristic
124C2×C4⋊Dic53C2311yescharacteristic
125C2×C4⋊Dic53C2311yescharacteristic
126C2×#11719919—21no—
127C2×#11719919—21no—
128C2×#11719919—21no—
129C2×#11719919—21no—
130C2×#11719919—21no—
131C2×#11719919—21no—
132C2×#11719919—21no—
133C2×C22⋊Dic53—21no—
134C2×C22⋊Dic53—21no—
135C2×C22⋊Dic53—21no—
136C2×C22⋊Dic53—21no—
137C2×#11719921—21no—
138C2×#11719921—21no—
139C2×#11719921—21no—
140C2×C4×Dic53—21no—
141C2×C4×Dic53—21no—
142C2×C4×Dic53—21no—
143#13133151C2314yes—
144#13133151C2314yes—
145#13133151C2314yes—
146#13133151C2314yes—
147#13133149C2314yes—
148#13133149C2314yes—
149#13133149C2314yes—
150#13133149C2314yes—
151#13133149C2314yes—
152#13133142C2314yes—
153#13133142C2314yes—
154#13133142C2314yes—
155#13133139C2314yes—
156#13133139C2314yes—
157#13133139C2314yes—
158C22×D4×C53D411yescharacteristic
159C23×C4×C53C2311yescharacteristic
160C23×C4×C53C2311yescharacteristic
161C2×M16×C53—24no—
162C2×M16×C53—24no—
163C2×M16×C53C2314yes—
164C2×M16×C53C2314yes—
165C22×C8×C53C2311yescharacteristic
166C22×C8×C53C2311yescharacteristic
167C22×C8×C53C2311yescharacteristic
168C22×C8×C53C2311yescharacteristic
169C4×D4×C53D414yes—
170C4×D4×C53C2314yes—
171C2×C4⋊C4×C53D411yescharacteristic
172C2×C22⋊C4×C53D411yescharacteristic
173C2×C22⋊C4×C53D411yescharacteristic
174C2×C42×C53C2311yescharacteristic
175C4⋊C8×C53C2314yes—
176C22⋊C8×C53C2314yes—
177C22⋊C8×C53C2314yes—
178C4×C8×C53C2314yes—
179C24×C53C2×D411yescharacteristic
180C24×C53C2×D411yescharacteristic
181C23×D53—21no—
182C2×D4×C53—42no—
183C2×D4×C53C2×D414yes—
184C22×C4×C53—22no—
185C22×C4×C53—22no—
186C22×C4×C53—22no—
187C22×C4×C53—22no—
188C22×C4×C53C2×D411yescharacteristic
189C22×C4×C53C2×D411yescharacteristic
190C22×C4×C53C2×D411yescharacteristic
191C22×C4×C53C2×D411yescharacteristic
192C22×C4×C53C2×D412yes—
193C22×C4×C53C2×D412yes—
194C22×C4×C53C2412yes—
195C22×C4×C53C2412yes—
196C22×C4×C53C2411yescharacteristic
197C2×C22⋊D53—24no—
198C2×C22⋊D53—24no—
199C2×C22⋊D53—44no—
200C2×C22⋊D53—82no—
201C22×Dic53—21no—
202C22×Dic53—21no—
203C22×Dic53—21no—
204C22×Dic53—21no—
205C22×Dic53—21no—
206C22×Dic53—21no—
207C22×Dic53—21no—
208C22×Dic53—24no—
209C22×Dic53—24no—
210C22×Dic53—44no—
211C22×Dic53—82no—
212C2×D212—22no—
213C2×D212—22no—
214C2×D212—21no—
215C2×D212C2412yes—
216C2×C4×D53—24no—
217C2×C4×D53—82no—
218C2×Dic106—22no—
219C2×Dic106—22no—
220C2×Dic106—21no—
221C2×Dic106C2412yes—
222M16×C53—28no—
223M16×C53—28no—
224C2×C8×C53—22no—
225C2×C8×C53—22no—
226C2×C8×C53—22no—
227C2×C8×C53#4114yes—
228C2×C8×C53C2412yes—
229C2×C8×C53C2412yes—
230C2×C8×C53C2412yes—
231C2×C8×C53C2412yes—
232C4⋊C4×C53C2×D414yes—
233C22⋊C4×C53C2×D414yes—
234C22⋊C4×C53C2×D414yes—
235C42×C53C2×D412yes—
236C42×C53C2412yes—
237C22⋊Dic53—24no—
238C22⋊Dic53—24no—
239C22⋊Dic53—24no—
240C22⋊Dic53—24no—
241#11719921—24no—
242#11719921—24no—
243#11719921—24no—
244C4⋊Dic53—21no—
245C4⋊Dic53—21no—
246C4⋊Dic53—21no—
247C4⋊Dic53—21no—
248C4⋊Dic53—24no—
249C4⋊Dic53—24no—
250C4⋊Dic53—21no—
251C4⋊Dic53—21no—
252C4⋊Dic53C2412yes—
253C4⋊Dic53C2412yes—
254C4⋊Dic53C2412yes—
255C4⋊Dic53C2412yes—
256C4⋊Dic53C2412yes—
257C4⋊Dic53C2412yes—
258#11719919—24no—
259#11719919—24no—
260#11719919—24no—
261#11719919—24no—
262#11719919—24no—
263#11719919—24no—
264#11719919—24no—
265C4×Dic53—24no—
266C4×Dic53—24no—
267C4×Dic53—24no—
268#11719913—28no—
269C23×C53—22no—
270C23×C53—22no—
271C23×C53—22no—
272C23×C53—22no—
273C23×C53—22no—
274C23×C53—22no—
275C23×C53C22×D412yes—
276C23×C53C22×D412yes—
277C23×C53C22×D411yescharacteristic
278C22×D53—22no—
279C22×D53—42no—
280C22×D53—42no—
281C22×D53—42no—
282D4×C53—44no—
283C2×C4×C53—22no—
284C2×C4×C53—22no—
285C2×C4×C53—22no—
286C2×C4×C53—22no—
287C2×C4×C53—24no—
288C2×C4×C53—24no—
289C2×C4×C53—22no—
290C2×C4×C53—22no—
291C2×C4×C53—22no—
292C2×C4×C53—22no—
293C2×C4×C53C22×D412yes—
294C2×C4×C53C22×D412yes—
295C2×C4×C53C22×D412yes—
296C2×C4×C53C22×D412yes—
297C2×C4×C53C22×D411yescharacteristic
298C2×C4×C53C2×#4112yes—
299C2×C4×C532−1+412yes—
300C2×C4×C53C2511yescharacteristic
301C22⋊D53—48no—
302C22⋊D53—84no—
303C2×Dic53—22no—
304C2×Dic53—22no—
305C2×Dic53—22no—
306C2×Dic53—22no—
307C2×Dic53—22no—
308C2×Dic53—22no—
309C2×Dic53—22no—
310C2×Dic53—48no—
311C2×Dic53—42no—
312C2×Dic53—42no—
313C2×Dic53—42no—
314C2×Dic53—42no—
315C2×Dic53—42no—
316C2×Dic53—42no—
317C2×Dic53—42no—
318C2×Dic53—84no—
319D212—22no—
320D212—22no—
321D212—42no—
322C4×D53—84no—
323Dic106—22no—
324Dic106—22no—
325Dic106—42no—
326C8×C53—22no—
327C8×C53—22no—
328C8×C53—22no—
329C8×C53C2×#4114yes—
330C2×#3351—531nomaximal, Sylow
331C22×C53—22no—
332C22×C53—22no—
333C22×C53—22no—
334C22×C53—22no—
335C22×C53—22no—
336C22×C53—22no—
337C22×C53—44no—
338C22×C53—44no—
339C22×C53#54712yes—
340C22×C53#57512yes—
341C22×C53#57712yes—
342C22×C53C23×D411yescharacteristic
343C2×D53—42no—
344C2×D53—42no—
345C2×D53—42no—
346C2×D53—84no—
347C4×C53—22no—
348C4×C53—22no—
349C4×C53—22no—
350C4×C53—22no—
351C4×C53#54712yes—
352C4×C53C22×#4111yescharacteristic
353C4×C53C2×2−1+411yescharacteristic
354Dic53—42no—
355Dic53—42no—
356Dic53—42no—
357Dic53—42no—
358Dic53—42no—
359Dic53—42no—
360Dic53—42no—
361C2×#553—531no—
362C2×#552—531no—
363#3351—5316no—
364C2×#499—531no—
365C2×#481—531no—
366C2×#485—531no—
367C2×#482—531no—
368C2×#483—531no—
369C2×#479—531no—
370C2×#478—531no—
371C2×#468—531no—
372C2×#468—531no—
373C2×C4×SD16—531no—
374C2×#436D5311yescharacteristic, complemented
375C2×#428—531no—
376C2×#428—531no—
377C2×C53—42no—
378C2×C53—42no—
379C2×C53#335114yescomplemented
380C2×C53C2×#54711yescharacteristic
381C2×C53C2×#57511yescharacteristic
382C2×C53C2×#57711yescharacteristic
383D53—82no—
384C22×SD16—531no—
385C22×M16C2×D5311yescharacteristic
386C22×M16C2×D5311yescharacteristic
387#553—538no—
388#553—1064no—
389#552—538no—
390#552—1064no—
391C2×#126—1061no—
392C2×#126—1061no—
393C2×#125—531no—
394C2×#125—531no—
395C2×#125—1061no—
396C2×#123—1061no—
397C2×#123—1061no—
398C2×C22⋊Q8—531no—
399C2×C22⋊Q8—531no—
400C2×#121—531no—
401C2×#121—531no—
402C2×#121—1061no—
403C2×C4×Q8—531no—
404C2×C4×D4—531no—
405C2×C4×D4—1061no—
406C2×C4×D4C2×D5311yescharacteristic
407C2×#117—531no—
408C2×#117—531no—
409C2×#117—1061no—
410C22×C4⋊C4—531no—
411C22×C4⋊C4—531no—
412#499—538no—
413#485—538no—
414#483—538no—
415#482—538no—
416#481—538no—
417#479—538no—
418#478—538no—
419#468—538no—
420#468—538no—
421C4×SD16—538no—
422#436C2×D5318yescomplemented
423#428—538no—
424#428—538no—
425C2×#107—531no—
426C2×#107—531no—
427C2×#107—531no—
428C2×#107—531no—
429C2×#106—531no—
430C2×#106—531no—
431C2×#106—531no—
432C2×#106—531no—
433C2×#106—531no—
434C2×C4⋊C8C2×D5311yescharacteristic
435C2×#103—531no—
436C2×#103—531no—
437C2×#103—531no—
438C2×#102—531no—
439C2×#102—531no—
440C2×#102—531no—
441C2×C22⋊C8C2×D5311yescharacteristic
442C2×C22⋊C8C2×D5311yescharacteristic
443C2×C4×C8C2×D5311yescharacteristic
444C53C2×#335111yescharacteristic, complemented, Sylow
445C22×Q8—531no—
446C22×D4—531no—
447C22×D4—1061no—
448C22×D4—1061no—
449C22×D4D21211yescharacteristic
450C23×C4—1061no—
451C23×C4—1061no—
452C23×C4—1061no—
453C23×C4C22×D5311yescharacteristic
454C23×C4C22×D5311yescharacteristic
455C2×SD16—534no—
456C2×SD16—1064no—
457C2×M16—24no—
458C2×M16—24no—
459C2×M16C22×D5314yes—
460C2×M16C22×D5314yes—
461C22×C8C22×D5311yescharacteristic
462C22×C8C22×D5311yescharacteristic
463C22×C8C22×D5311yescharacteristic
464C22×C8C22×D5311yescharacteristic
465#126—1068no—
466#126—1068no—
467#125—534no—
468#125—534no—
469#125—1068no—
470#125—1062no—
471#125—1062no—
472#123—1068no—
473#123—1068no—
474C22⋊Q8—534no—
475C22⋊Q8—534no—
476C22⋊Q8—1062no—
477C22⋊Q8—1062no—
478#121—534no—
479#121—534no—
480#121—1068no—
481#121—1062no—
482#121—1062no—
483C4×Q8—534no—
484C4×Q8—1062no—
485C4×D4—534no—
486C4×D4—1068no—
487C4×D4—1062no—
488C4×D4D21214yes—
489C4×D4C22×D5314yes—
490#117—534no—
491#117—534no—
492#117—1062no—
493#117—1062no—
494#117—1068no—
495C2×C4⋊C4—531no—
496C2×C4⋊C4—531no—
497C2×C4⋊C4—531no—
498C2×C4⋊C4—531no—
499C2×C4⋊C4—534no—
500C2×C4⋊C4—534no—
501C2×C4⋊C4—531no—
502C2×C4⋊C4—531no—
503C2×C4⋊C4—1061no—
504C2×C4⋊C4—1061no—
505C2×C4⋊C4—1062no—
506C2×C4⋊C4—1062no—
507C2×C4⋊C4—1061no—
508C2×C4⋊C4—1061no—
509C2×C4⋊C4—1061no—
510C2×C4⋊C4—1061no—
511C2×C4⋊C4—1061no—
512C2×C4⋊C4—1061no—
513C2×C4⋊C4—1061no—
514C2×C4⋊C4D21211yescharacteristic
515C2×C22⋊C4—1061no—
516C2×C22⋊C4—1061no—
517C2×C22⋊C4—1061no—
518C2×C22⋊C4—1061no—
519C2×C22⋊C4—1061no—
520C2×C22⋊C4—1061no—
521C2×C22⋊C4—1061no—
522C2×C22⋊C4D21211yescharacteristic
523C2×C22⋊C4D21211yescharacteristic
524C2×C42—1061no—
525C2×C42—1061no—
526C2×C42—1061no—
527C2×C42C22×D5311yescharacteristic
528#107—534no—
529#107—534no—
530#107—534no—
531#107—534no—
532#106—534no—
533#106—534no—
534#106—534no—
535#106—534no—
536#106—534no—
537C4⋊C8C22×D5314yes—
538#103—534no—
539#103—534no—
540#103—534no—
541#102—534no—
542#102—534no—
543#102—534no—
544C22⋊C8C22×D5314yes—
545C22⋊C8C22×D5314yes—
546C4×C8C22×D5314yes—
547C24—1061no—
548C24C2×D21211yescharacteristic
549C24C2×D21211yescharacteristic
550C2×Q8—532no—
551C2×Q8—1061no—
552C2×Q8—1062no—
553C2×Q8—1062no—
554C2×D4—42no—
555C2×D4—532no—
556C2×D4—1064no—
557C2×D4—1064no—
558C2×D4—1061no—
559C2×D4—1062no—
560C2×D4—1062no—
561C2×D4—4242no—
562C2×D4—2124no—
563C2×D4C2×D21214yes—
564C22×C4—22no—
565C22×C4—22no—
566C22×C4—22no—
567C22×C4—22no—
568C22×C4—1064no—
569C22×C4—1064no—
570C22×C4—1061no—
571C22×C4—1061no—
572C22×C4—1061no—
573C22×C4—1061no—
574C22×C4—1061no—
575C22×C4—1061no—
576C22×C4—1061no—
577C22×C4—1064no—
578C22×C4—4242no—
579C22×C4—4242no—
580C22×C4—2124no—
581C22×C4C2×D21212yes—
582C22×C4C2×D21212yes—
583C22×C4C2×D21211yescharacteristic
584C22×C4C2×D21211yescharacteristic
585C22×C4C2×D21211yescharacteristic
586C22×C4C2×D21211yescharacteristic
587C22×C4C23×D5312yes—
588C22×C4C23×D5312yes—
589C22×C4C23×D5311yescharacteristic
590SD16—1068no—
591M16—28no—
592M16—28no—
593C2×C8—22no—
594C2×C8—22no—
595C2×C8—22no—
596C2×C8#1171994714yes—
597C2×C8C23×D5312yes—
598C2×C8C23×D5312yes—
599C2×C8C23×D5312yes—
600C2×C8C23×D5312yes—
601C4⋊C4—532no—
602C4⋊C4—532no—
603C4⋊C4—532no—
604C4⋊C4—532no—
605C4⋊C4—532no—
606C4⋊C4—532no—
607C4⋊C4—1061no—
608C4⋊C4—1061no—
609C4⋊C4—1061no—
610C4⋊C4—1061no—
611C4⋊C4—1064no—
612C4⋊C4—1064no—
613C4⋊C4—1061no—
614C4⋊C4—1061no—
615C4⋊C4—1064no—
616C4⋊C4—1064no—
617C4⋊C4—1064no—
618C4⋊C4—1064no—
619C4⋊C4—1064no—
620C4⋊C4—1064no—
621C4⋊C4—1064no—
622C4⋊C4C2×D21214yes—
623C22⋊C4—1064no—
624C22⋊C4—1064no—
625C22⋊C4—1064no—
626C22⋊C4—1064no—
627C22⋊C4—1064no—
628C22⋊C4—1064no—
629C22⋊C4—1064no—
630C22⋊C4C2×D21214yes—
631C22⋊C4C2×D21214yes—
632C42—1064no—
633C42—1064no—
634C42—1064no—
635C42C2×D21212yes—
636C42C23×D5312yes—
637C23—22no—
638C23—22no—
639C23—22no—
640C23—22no—
641C23—22no—
642C23—22no—
643C23—1062no—
644C23—2122no—
645C23—2122no—
646C23—2122no—
647C23C22×D21212yes—
648C23C22×D21212yes—
649C23C22×D21211yescharacteristic
650Q8—1062no—
651Q8—1062no—
652Q8—2122no—
653D4—44no—
654D4—1062no—
655D4—1062no—
656D4—4244no—
657D4—2128no—
658D4—2122no—
659C2×C4—22no—
660C2×C4—22no—
661C2×C4—22no—
662C2×C4—22no—
663C2×C4—24no—
664C2×C4—24no—
665C2×C4—22no—
666C2×C4—22no—
667C2×C4—22no—
668C2×C4—22no—
669C2×C4—1062no—
670C2×C4—1062no—
671C2×C4—1062no—
672C2×C4—1062no—
673C2×C4—1062no—
674C2×C4—1062no—
675C2×C4—1062no—
676C2×C4—4244no—
677C2×C4—4244no—
678C2×C4—2128no—
679C2×C4—2122no—
680C2×C4—2122no—
681C2×C4—2122no—
682C2×C4—2122no—
683C2×C4—2122no—
684C2×C4—2122no—
685C2×C4—2122no—
686C2×C4C22×D21212yes—
687C2×C4C22×D21212yes—
688C2×C4C22×D21212yes—
689C2×C4C22×D21212yes—
690C2×C4C22×D21211yescharacteristic
691C2×C4C2×#1171994712yes—
692C2×C4#1313326412yes—
693C2×C4C24×D5311yescharacteristic
694C8—22no—
695C8—22no—
696C8—22no—
697C8C2×#1171994714yes—
698C22—22no—
699C22—22no—
700C22—22no—
701C22—22no—
702C22—22no—
703C22—22no—
704C22—44no—
705C22—44no—
706C22—4244no—
707C22—2122no—
708C22—2122no—
709C22—2122no—
710C22#1681127712yes—
711C22#1681142312yes—
712C22#1681143512yes—
713C22C23×D21211yescharacteristic
714C4—22no—
715C4—22no—
716C4—22no—
717C4—22no—
718C4—2122no—
719C4—2122no—
720C4—2122no—
721C4—2122no—
722C4—2122no—
723C4—2122no—
724C4—2122no—
725C4#1681127712yes—
726C4C22×#1171994711yescharacteristic
727C4C2×#1313326411yescharacteristic
728C2—42no—
729C2—42no—
730C2—4242no—
731C2#2028727714yesdirect product factor
732C2C2×#1681127711yescharacteristic
733C2C2×#1681142311yescharacteristic
734C2C2×#1681143511yescharacteristic
subgroupG/H
centerC23C22×D212
commutator, cosocleC2×C4×C53C25
FrattiniC2×C4C24×D53
FittingC2×C53×#436C2
socleC23×C53C22×D4
prime radicalC2×#16811319C2
hypercenterC2×#436D53
hypocenterC53C2×#3351
LCSG ▷ C2×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#436

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. C2×#16811313C2semidirect
3. #20287277C2direct (N × H)
4. C2×#16811025C2semidirect
5. C2×#16810942C2semidirect
6. C2×#16810965C2semidirect
7. C2×#16810948C2semidirect
8. C2×#16810954C2semidirect
9. C2×#16810931C2semidirect
10. C2×#16810924C2semidirect
11. C2×#16810869C2semidirect
12. C2×#16810869C2semidirect
13. C2×C4×#11719913C2semidirect
14. C2×#16810665C2semidirect
15. C2×#16810665C2semidirect
16. C2×C53×#436C2semidirect
21. #16811313C22semidirect
42. #16811025C22semidirect
43. #16810965C22semidirect
44. #16810954C22semidirect
45. #16810948C22semidirect
46. #16810942C22semidirect
47. #16810931C22semidirect
48. #16810924C22semidirect
49. #16810869C22semidirect
50. #16810869C22semidirect
51. C4×#11719913C22semidirect
52. #16810665C22semidirect
53. #16810665C22semidirect
72. C53×#436C22semidirect
374. C2×#436D53semidirect
379. C2×C53#3351semidirect
422. #436C2×D53semidirect
444. C53C2×#3351semidirect
731. C2#20287277direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C2×#168113192
C2×#168113132
#202872772
C2×#168110252
C2×#168109422
C2×#168109652
C2×#168109482
C2×#168109542
C2×#168109312
C2×#168109242
C2×#168108692
C2×C4×#117199132
C2×#168106652
C2×C53×#4362
C2×#335153